objetivos

i) did abundance of tadpoles differ between streams?

We captured and measured 1687 tadpoles o A. eugenioi in the two streams sampled. Tadpoles of A. eugenioi occurred in stream 1 during all 36 months of the study. In stream 2, tadpoles were found in 26 months and were more frequntly found in the dry season. The abundance of tadpoles in streams were heterocedastic and not normal, as it is visualized in boxplot and histogram. The analyses of the residuals of ANOVA indicated that the premisses of normality and homocedasticity were not met, so we use Kruskal-Wallis rank sum test (non-parametric ANOVA). Resutls indicated that the abundance of tadpoles difered significantly between streams.

##   Class Total
## 1     1    36
## 2     2    26
##        1  2
## dry   18 15
## rainy 18 11

##              Df Sum Sq Mean Sq F value   Pr(>F)    
## Stream        1   5805    5805   40.08 9.42e-10 ***
## Residuals   286  41426     145                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
##  Kruskal-Wallis rank sum test
## 
## data:  Abundance by Stream
## Kruskal-Wallis chi-squared = 40.731, df = 1, p-value = 1.747e-10

ii) did tadpoles of different class of development tend to occur more frequently and to be more abundant in the rainy or in the dry season?

Tadpoles of class I.2 were the most frequent being registered all months, followed by tadpoles of class II, I.1, and III. Except for tadpoles of class I.1 that was more frequent in the dry period, tadpoles of all other classes were more frequent in the rainy period.

##   Class Total
## 1   I.1    23
## 2   I.2    36
## 3    II    35
## 4   III    15
##     dry rainy
## I.1  14     9
## I.2  18    18
## II   17    18
## III   5    10

ii) did tadpoles of different class of development tend to occur more frequently and to be more abundant in the rainy or in the dry season (absolute and index of abundance, and mean abundance)?

We captured and measured 1687 tadpoles o A. eugenioi. The most common tadpoles belonged to class I.2 and the rarer to class III. Tadpoles of all development class were more abundant in the dry period both in absolute values, by the index and the mean. The exception were tadpoles of class I.2 that were more comomn in the rainy season.

##  I.1  I.2   II  III 
##   88 1322  251   26
##     dry rainy
## I.1  60    28
## I.2 559   763
## II  165    86
## III  14    12
##            dry      rainy
## I.1  2.0000000  0.9333333
## I.2 18.6333333 25.4333333
## II   5.5000000  2.8666667
## III  0.4666667  0.4000000
##            dry      rainy
## I.1  1.6666667  0.7777778
## I.2 15.5277778 21.1944444
## II   4.5833333  2.3888889
## III  0.3888889  0.3333333

ii) did tadpoles of different class of development tend to occur more frequently and to be more abundant in the rainy or in the dry season? ANOVA of the abundance of all tadpoles between seasons

Both absolut abundances, the index, and mean abundance showed evidences of heterocedasticity and lack of normality bewteen seasons, as it is visualized in boxplot and histogram. The results of ANOVA indicated no differences in abudances between seasons. The analyses of residuals indicated that the premisses of normality and homocedasticity were not met.

##              Df Sum Sq Mean Sq F value Pr(>F)
## Season        1     58    57.5   0.176  0.676
## Residuals   142  46444   327.1

##              Df Sum Sq Mean Sq F value Pr(>F)
## Season        1   0.06  0.0639   0.176  0.676
## Residuals   142  51.60  0.3634

##              Df Sum Sq Mean Sq F value Pr(>F)
## Season        1     14   14.38   0.176  0.676
## Residuals   142  11611   81.77

## ii) did tadpoles of different class of development tend to occur more frequently and to be more abundant in the rainy or in the dry season? ANOVA of the abundance of tadpoles of Class I.1 between seasons

The boxplot sugests the presence of outliers and heterocedasticity. The histogram indicates lack of normality as expected for counts. The test of ANOVA indicate no difference in abundances between seasons. However, plots of the residuals indicated that the premisses of normality and homocedasticity were not matched. Resutls were consistent for both absolute, the index of abundance, and mean abundance.

##                                      Df Sum Sq Mean Sq F value Pr(>F)
## abund1$Season[abund1$Class == "I.1"]  1   28.4   28.44   2.477  0.125
## Residuals                            34  390.4   11.48

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abund1$Abundance[abund1$Class == "I.1"] by abund1$Season[abund1$Class == "I.1"]
## Kruskal-Wallis chi-squared = 2.9843, df = 1, p-value = 0.08408

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abund.ind$Abundance[abund.ind$Class == "I.1"] by abund.ind$Season[abund.ind$Class == "I.1"]
## Kruskal-Wallis chi-squared = 2.9843, df = 1, p-value = 0.08408

##                                              Df Sum Sq Mean Sq F value
## abund.mean$Season[abund.mean$Class == "I.1"]  1   7.11   7.111   2.477
## Residuals                                    34  97.61   2.871        
##                                              Pr(>F)
## abund.mean$Season[abund.mean$Class == "I.1"]  0.125
## Residuals

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abund.mean$Mean[abund.mean$Class == "I.1"] by abund.mean$Season[abund.mean$Class == "I.1"]
## Kruskal-Wallis chi-squared = 2.9843, df = 1, p-value = 0.08408

ii) did tadpoles of different class of development tend to occur more frequently and to be more abundant in the rainy or in the dry season? ANOVA of the abundance of tadpoles of Class I.2 between seasons

The boxplot sugests the presence of heterocedasticity. The histogram indicates lack of normality as expected for counts. The test of ANOVA indicate no difference in abundances between seasons. The plots of the residuals indicated that the premisses of normality and homocedasticity were not matched. Resutls were consistent for both absolute, the index of abundance, and mean abundance.

##                                      Df Sum Sq Mean Sq F value Pr(>F)  
## abund1$Season[abund1$Class == "I.2"]  1   1156  1156.0   3.329 0.0769 .
## Residuals                            34  11805   347.2                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abund1$Abundance[abund1$Class == "I.2"] by abund1$Season[abund1$Class == "I.2"]
## Kruskal-Wallis chi-squared = 2.1217, df = 1, p-value = 0.1452

##                                            Df Sum Sq Mean Sq F value
## abund.ind$Season[abund.ind$Class == "I.2"]  1  1.284  1.2844   3.329
## Residuals                                  34 13.117  0.3858        
##                                            Pr(>F)  
## abund.ind$Season[abund.ind$Class == "I.2"] 0.0769 .
## Residuals                                          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abund.ind$Abundance[abund.ind$Class == "I.2"] by abund.ind$Season[abund.ind$Class == "I.2"]
## Kruskal-Wallis chi-squared = 2.0304, df = 1, p-value = 0.1542

##                                              Df Sum Sq Mean Sq F value
## abund.mean$Season[abund.mean$Class == "I.2"]  1    289   289.0   3.329
## Residuals                                    34   2951    86.8        
##                                              Pr(>F)  
## abund.mean$Season[abund.mean$Class == "I.2"] 0.0769 .
## Residuals                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abund.mean$Mean[abund.mean$Class == "I.2"] by abund.mean$Season[abund.mean$Class == "I.2"]
## Kruskal-Wallis chi-squared = 2.1217, df = 1, p-value = 0.1452

ii) did tadpoles of different class of development tend to occur more frequently and to be more abundant in the rainy or in the dry season? ANOVA of the abundance of tadpoles of Class II between seasons

The boxplot sugests the presence of outliers and heterocedasticity. The histogram indicates lack of normality as expected for counts. The test of ANOVA indicate no difference in abundances between seasons. The plots of the residuals indicated that the premisses of normality and homocedasticity were not matched. Resutls were consistent for both absolute, the index of abundance, and mean abundance.

##                                     Df Sum Sq Mean Sq F value Pr(>F)
## abund1$Season[abund1$Class == "II"]  1  173.4  173.36   2.768  0.105
## Residuals                           34 2129.6   62.64

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abund1$Abundance[abund1$Class == "II"] by abund1$Season[abund1$Class == "II"]
## Kruskal-Wallis chi-squared = 0.07337, df = 1, p-value = 0.7865

##                                           Df Sum Sq Mean Sq F value Pr(>F)
## abund.ind$Season[abund.ind$Class == "II"]  1 0.1926  0.1926   2.768  0.105
## Residuals                                 34 2.3662  0.0696

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abund.ind$Abundance[abund.ind$Class == "II"] by abund.ind$Season[abund.ind$Class == "II"]
## Kruskal-Wallis chi-squared = 0.09165, df = 1, p-value = 0.7621

##                                             Df Sum Sq Mean Sq F value
## abund.mean$Season[abund.mean$Class == "II"]  1   43.3   43.34   2.768
## Residuals                                   34  532.4   15.66        
##                                             Pr(>F)
## abund.mean$Season[abund.mean$Class == "II"]  0.105
## Residuals

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abund.mean$Mean[abund.mean$Class == "II"] by abund.mean$Season[abund.mean$Class == "II"]
## Kruskal-Wallis chi-squared = 0.07337, df = 1, p-value = 0.7865

ii) did tadpoles of different class of development tend to occur more frequently and to be more abundant in the rainy or in the dry season? ANOVA of the abundance of tadpoles of Class III between seasons

The boxplot sugests the presence of outliers and heterocedasticity. The histogram indicates lack of normality as expected for counts. The test of ANOVA indicate no difference in abundances between seasons. The plots of the residuals indicated that the premisses of normality and homocedasticity were not matched. Resutls were consistent for both absolute, the index of abundance, and mean abundance.

##                                      Df Sum Sq Mean Sq F value Pr(>F)
## abund1$Season[abund1$Class == "III"]  1   0.11  0.1111   0.074  0.787
## Residuals                            34  51.11  1.5033

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abund1$Abundance[abund1$Class == "III"] by abund1$Season[abund1$Class == "III"]
## Kruskal-Wallis chi-squared = 1.2843, df = 1, p-value = 0.2571

##                                            Df  Sum Sq   Mean Sq F value
## abund.ind$Season[abund.ind$Class == "III"]  1 0.00012 0.0001235   0.074
## Residuals                                  34 0.05679 0.0016703        
##                                            Pr(>F)
## abund.ind$Season[abund.ind$Class == "III"]  0.787
## Residuals

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abund.ind$Abundance[abund.ind$Class == "III"] by abund.ind$Season[abund.ind$Class == "III"]
## Kruskal-Wallis chi-squared = 1.2843, df = 1, p-value = 0.2571

##                                              Df Sum Sq Mean Sq F value
## abund.mean$Season[abund.mean$Class == "III"]  1  0.028  0.0278   0.074
## Residuals                                    34 12.778  0.3758        
##                                              Pr(>F)
## abund.mean$Season[abund.mean$Class == "III"]  0.787
## Residuals

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abund.mean$Mean[abund.mean$Class == "III"] by abund.mean$Season[abund.mean$Class == "III"]
## Kruskal-Wallis chi-squared = 1.2843, df = 1, p-value = 0.2571

ii) did tadpoles of different class of development from each stream tend to occur more frequently and to be more abundant in the rainy or in the dry season? ANOVA of the abundance of tadpoles of different classes between seasons in stream 1

In stream 1, tadpoles of class I.1 were the second least abundant (4.1%, n = 61). They were more frequent (30.5%, n = 11 months) and abundant (2.5%, n = 38) in the dry period. We found no statistical differences in abundances of tadpoles of class I.1 between seasons (F2.34 = 1.146, p = 0.292). Tadpoles of class I.2 occurred in all months and were the most abundant, representing 80.5% (n = 1199) of all tadpoles found in stream 1. We registered their highest abundance in the rainy season (48.5%, n = 716). Tadpoles of class I.2 were statisticaly more abundant in the rainy period (F2.34 = 4.705, p = 0.037). Tadpoles of class II the second most abundant (14.2%, n = 212) and frequent (n = 30 months). They were found more frequently during the rainy season (47.2%, n = 17), but we registered their highest abundance in the dry season (9.2%, n = 137). We did not find statistical differences in the abundances of tadpoles of class II between seasons (X2 = 0.004, p = 0.949). Tadpoles of class III (final stage of metamorphose) were the least abundant in stream 1 with only 18 individuals (1.2%) and occurred more frequnetly in the rainy season (25%, n = 9 months). We did not find significant difference in the number of tadpoles of class III between seasons (F2. = 0.569, p = 0.456).

## , , 1
## 
##     dry rainy
## I.1  11     7
## I.2  18    18
## II   13    17
## III   3     9
## 
## , , 2
## 
##     dry rainy
## I.1   6     4
## I.2  13     9
## II   10     6
## III   3     1
## , , 1
## 
##            dry     rainy
## I.1 0.30555556 0.1944444
## I.2 0.50000000 0.5000000
## II  0.36111111 0.4722222
## III 0.08333333 0.2500000
## 
## , , 2
## 
##            dry      rainy
## I.1 0.16666667 0.11111111
## I.2 0.36111111 0.25000000
## II  0.27777778 0.16666667
## III 0.08333333 0.02777778
##        1   2
## I.1   61  27
## I.2 1199 123
## II   212  39
## III   18   8
##              1           2
## I.1 0.04093960 0.018120805
## I.2 0.80469799 0.082550336
## II  0.14228188 0.026174497
## III 0.01208054 0.005369128
##              1          2
## I.1 0.30964467 0.13705584
## I.2 6.08629442 0.62436548
## II  1.07614213 0.19796954
## III 0.09137056 0.04060914
## , , 1
## 
##     dry rainy
## I.1  38    23
## I.2 483   716
## II  137    75
## III   7    11
## 
## , , 2
## 
##     dry rainy
## I.1  22     5
## I.2  76    47
## II   28    11
## III   7     1
## , , 1
## 
##             dry      rainy
## I.1 0.025503356 0.01543624
## I.2 0.324161074 0.48053691
## II  0.091946309 0.05033557
## III 0.004697987 0.00738255
## 
## , , 2
## 
##             dry        rainy
## I.1 0.014765101 0.0033557047
## I.2 0.051006711 0.0315436242
## II  0.018791946 0.0073825503
## III 0.004697987 0.0006711409

## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
##  extra argument 'p.adj' will be disregarded
##                                                        Df Sum Sq Mean Sq
## abund$Season[abund$Class == "I.1" & abund$Stream == 1]  1   6.25   6.250
## Residuals                                              34 185.39   5.453
##                                                        F value Pr(>F)
## abund$Season[abund$Class == "I.1" & abund$Stream == 1]   1.146  0.292
## Residuals

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abund$Abundance[abund$Class == "I.1" & abund$Stream == 1] by abund$Season[abund$Class == "I.1" & abund$Stream == 1]
## Kruskal-Wallis chi-squared = 1.659, df = 1, p-value = 0.1977

##                                                        Df Sum Sq Mean Sq
## abund$Season[abund$Class == "I.2" & abund$Stream == 1]  1   1508  1508.0
## Residuals                                              34  10898   320.5
##                                                        F value Pr(>F)  
## abund$Season[abund$Class == "I.2" & abund$Stream == 1]   4.705 0.0372 *
## Residuals                                                              
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abund$Abundance[abund$Class == "I.2" & abund$Stream == 1] by abund$Season[abund$Class == "I.2" & abund$Stream == 1]
## Kruskal-Wallis chi-squared = 3.3708, df = 1, p-value = 0.06636

##                                                       Df Sum Sq Mean Sq
## abund$Season[abund$Class == "II" & abund$Stream == 1]  1  106.8  106.78
## Residuals                                             34 1562.8   45.96
##                                                       F value Pr(>F)
## abund$Season[abund$Class == "II" & abund$Stream == 1]   2.323  0.137
## Residuals

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abund$Abundance[abund$Class == "II" & abund$Stream == 1] by abund$Season[abund$Class == "II" & abund$Stream == 1]
## Kruskal-Wallis chi-squared = 0.0040536, df = 1, p-value = 0.9492

##                                                        Df Sum Sq Mean Sq
## abund$Season[abund$Class == "III" & abund$Stream == 1]  1  0.444  0.4444
## Residuals                                              34 26.556  0.7810
##                                                        F value Pr(>F)
## abund$Season[abund$Class == "III" & abund$Stream == 1]   0.569  0.456
## Residuals

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abund$Abundance[abund$Class == "III" & abund$Stream == 1] by abund$Season[abund$Class == "III" & abund$Stream == 1]
## Kruskal-Wallis chi-squared = 3.1458, df = 1, p-value = 0.07612

ii) did tadpoles of different class of development from each stream tend to occur more frequently and to be more abundant in the rainy or in the dry season? ANOVA of the abundance of tadpoles of different classes between seasons in stream 2

In stream 2, tadpoles of class I.1 were the second least abundant (13.7%, n = 27). They were more frequent (16.6%, n = 6 months) and abundant (11.2%, n = 22) in the dry period. We found no statistical differences in abundances of tadpoles of class I.1 between seasons (X2 = 0.818, p = 0.365). Tadpoles of class I.2 occurred were the most abundant, representing 62.4% (n = 123) of all tadpoles found in stream 2. They were more frequent (36.1%, n = 13) and abundant in the dry season (38.6%, n = 76). Tadpoles of class I.2 did not differ statisticaly between seasons (F2.34 = 1.183, R2 = 0.005, p = 0.284). Tadpoles of class II the second most abundant (19.8%, n = 39). They were more abundant (14.2%, n = 28) and found more frequently during the dry season (27.7%, n = 10). We did not find statistical differences in the abundances of tadpoles of class II between seasons (X2 = 1.837, p = 0.175). Tadpoles of class III (final stage of metamorphose) were the least abundant in stream 2 with only 8 individuals (4.1%) and occurred more frequnetly in the dry season (8.3%, n = 3 months) when they were also more abundant (3.5%, n = 7). We did not find significant difference in the number of tadpoles of class III between seasons (X2 = 1.1524, p = 0.283).

## , , 1
## 
##     dry rainy
## I.1  11     7
## I.2  18    18
## II   13    17
## III   3     9
## 
## , , 2
## 
##     dry rainy
## I.1   6     4
## I.2  13     9
## II   10     6
## III   3     1
## , , 1
## 
##            dry     rainy
## I.1 0.30555556 0.1944444
## I.2 0.50000000 0.5000000
## II  0.36111111 0.4722222
## III 0.08333333 0.2500000
## 
## , , 2
## 
##            dry      rainy
## I.1 0.16666667 0.11111111
## I.2 0.36111111 0.25000000
## II  0.27777778 0.16666667
## III 0.08333333 0.02777778
##        1   2
## I.1   61  27
## I.2 1199 123
## II   212  39
## III   18   8
##              1           2
## I.1 0.04093960 0.018120805
## I.2 0.80469799 0.082550336
## II  0.14228188 0.026174497
## III 0.01208054 0.005369128
##              1          2
## I.1 0.30964467 0.13705584
## I.2 6.08629442 0.62436548
## II  1.07614213 0.19796954
## III 0.09137056 0.04060914
## , , 1
## 
##     dry rainy
## I.1  38    23
## I.2 483   716
## II  137    75
## III   7    11
## 
## , , 2
## 
##     dry rainy
## I.1  22     5
## I.2  76    47
## II   28    11
## III   7     1
## , , 1
## 
##            dry      rainy
## I.1 0.19289340 0.11675127
## I.2 2.45177665 3.63451777
## II  0.69543147 0.38071066
## III 0.03553299 0.05583756
## 
## , , 2
## 
##            dry       rainy
## I.1 0.11167513 0.025380711
## I.2 0.38578680 0.238578680
## II  0.14213198 0.055837563
## III 0.03553299 0.005076142

## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
##  extra argument 'p.adj' will be disregarded
##                                                        Df Sum Sq Mean Sq
## abund$Season[abund$Class == "I.1" & abund$Stream == 2]  1   8.03   8.028
## Residuals                                              34 134.72   3.962
##                                                        F value Pr(>F)
## abund$Season[abund$Class == "I.1" & abund$Stream == 2]   2.026  0.164
## Residuals

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abund$Abundance[abund$Class == "I.1" & abund$Stream == 2] by abund$Season[abund$Class == "I.1" & abund$Stream == 2]
## Kruskal-Wallis chi-squared = 0.81878, df = 1, p-value = 0.3655

##                                                        Df Sum Sq Mean Sq
## abund$Season[abund$Class == "I.2" & abund$Stream == 2]  1   23.4   23.36
## Residuals                                              34  671.4   19.75
##                                                        F value Pr(>F)
## abund$Season[abund$Class == "I.2" & abund$Stream == 2]   1.183  0.284
## Residuals
## 
## Call:
## lm(formula = abund$Abundance[abund$Class == "I.2" & abund$Stream == 
##     2] ~ abund$Season[abund$Class == "I.2" & abund$Stream == 
##     2])
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -4.222 -2.611 -1.417  1.931 10.778 
## 
## Coefficients:
##                                                             Estimate
## (Intercept)                                                    4.222
## abund$Season[abund$Class == "I.2" & abund$Stream == 2]rainy   -1.611
##                                                             Std. Error
## (Intercept)                                                      1.047
## abund$Season[abund$Class == "I.2" & abund$Stream == 2]rainy      1.481
##                                                             t value
## (Intercept)                                                   4.031
## abund$Season[abund$Class == "I.2" & abund$Stream == 2]rainy  -1.088
##                                                             Pr(>|t|)    
## (Intercept)                                                 0.000296 ***
## abund$Season[abund$Class == "I.2" & abund$Stream == 2]rainy 0.284389    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.444 on 34 degrees of freedom
## Multiple R-squared:  0.03363,    Adjusted R-squared:  0.005202 
## F-statistic: 1.183 on 1 and 34 DF,  p-value: 0.2844

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abund$Abundance[abund$Class == "I.2" & abund$Stream == 2] by abund$Season[abund$Class == "I.2" & abund$Stream == 2]
## Kruskal-Wallis chi-squared = 1.581, df = 1, p-value = 0.2086

##                                                       Df Sum Sq Mean Sq
## abund$Season[abund$Class == "II" & abund$Stream == 2]  1   8.03   8.028
## Residuals                                             34 168.72   4.962
##                                                       F value Pr(>F)
## abund$Season[abund$Class == "II" & abund$Stream == 2]   1.618  0.212
## Residuals

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abund$Abundance[abund$Class == "II" & abund$Stream == 2] by abund$Season[abund$Class == "II" & abund$Stream == 2]
## Kruskal-Wallis chi-squared = 1.8378, df = 1, p-value = 0.1752

##                                                        Df Sum Sq Mean Sq
## abund$Season[abund$Class == "III" & abund$Stream == 2]  1   1.00  1.0000
## Residuals                                              34  25.22  0.7418
##                                                        F value Pr(>F)
## abund$Season[abund$Class == "III" & abund$Stream == 2]   1.348  0.254
## Residuals

## 
##  Kruskal-Wallis rank sum test
## 
## data:  abund$Abundance[abund$Class == "III" & abund$Stream == 2] by abund$Season[abund$Class == "III" & abund$Stream == 2]
## Kruskal-Wallis chi-squared = 1.1524, df = 1, p-value = 0.2831

iii) did tadpoles of each class of development differ in body length between the two streams?

Tadpoles varied in body length and relative developmental stages along the study period in both streams (Figures 2A and 2B). Mean body length of tadpoles A. eugenioi from stream 1 were usually larger (Table 2). Class I.1 tadpoles of stream 1 were significantly larger in their body size in the first and second years (Mann-Whitney; U year 1 = 11686.5; pyear 1 = 0.01; Uyear2 = 18043; p year2 < 0.001), despites of the two maximum body sizes had occurred mainly in tadpoles of stream 2 (Table 2; Figures 2A and 2B). At least in stream 1, we monthly found tadpoles smaller than 7.0 mm (Figure 3). In class II tadpoles, the largest minimum body sizes of tadpoles were found in stream 1, while the largest maximum body sizes were encountered mainly in stream 2 (Table 2; Figures 2A and 2B). We did not find significant differences in body length of class II tadpoles between the two streams, although their body lengths were generally larger in stream 1 (Table 2; Figures 2A and 2B). Tadpoles of class III were usually larger at stream 1, except in the third year (Table 2; Figures 2A and 2B). Larger We registered minimum body sizes at class III in stream 1, and larger maximum body sizes mainly in stream 2 (Table 2; Figures 3 and 4). Statistical differences in tadpoles of class III could not be tested due to the small sample size.

##             1         2
## I.1  4.575410  3.929630
## I.2  8.871005  8.346281
## II  12.044498 11.430952
## III 14.633333 13.957143
##             1         2
## I.1 0.4299828 0.7378841
## I.2 2.2962050 2.0550361
## II  2.0943332 2.4707546
## III 1.0748461 2.3042404
##        1    2
## I.1  5.0  5.0
## I.2 15.9 16.6
## II  16.5 16.8
## III 17.5 17.6
##        1    2
## I.1  2.7  2.6
## I.2  5.1  5.1
## II   6.4  6.9
## III 13.0 11.9

##                                            Df Sum Sq Mean Sq F value
## bd.length$Stream[bd.length$Class == "I.1"]  1  7.805   7.805   26.58
## Residuals                                  86 25.249   0.294        
##                                              Pr(>F)    
## bd.length$Stream[bd.length$Class == "I.1"] 1.59e-06 ***
## Residuals                                              
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 10 observations deleted due to missingness
## 
## Call:
## lm(formula = bd.length$`Body length`[bd.length$Class == "I.1"] ~ 
##     bd.length$Stream[bd.length$Class == "I.1"])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.87541 -0.37541  0.07459  0.32459  1.07037 
## 
## Coefficients:
##                                             Estimate Std. Error t value
## (Intercept)                                  4.57541    0.06938  65.951
## bd.length$Stream[bd.length$Class == "I.1"]2 -0.64578    0.12525  -5.156
##                                             Pr(>|t|)    
## (Intercept)                                  < 2e-16 ***
## bd.length$Stream[bd.length$Class == "I.1"]2 1.59e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5418 on 86 degrees of freedom
##   (10 observations deleted due to missingness)
## Multiple R-squared:  0.2361, Adjusted R-squared:  0.2272 
## F-statistic: 26.58 on 1 and 86 DF,  p-value: 1.592e-06
## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
##  extra argument 'main' will be disregarded

## 
##  Kruskal-Wallis rank sum test
## 
## data:  bd.length$`Body length`[bd.length$Class == "I.1"] by bd.length$Stream[bd.length$Class == "I.1"]
## Kruskal-Wallis chi-squared = 14.725, df = 1, p-value = 0.0001244

##                                              Df Sum Sq Mean Sq F value
## bd.length$Stream[bd.length$Class == "I.2"]    1     30  30.227    5.84
## Residuals                                  1303   6744   5.176        
##                                            Pr(>F)  
## bd.length$Stream[bd.length$Class == "I.2"] 0.0158 *
## Residuals                                          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 10 observations deleted due to missingness
## 
## Call:
## lm(formula = bd.length$`Body length`[bd.length$Class == "I.2"] ~ 
##     bd.length$Stream[bd.length$Class == "I.2"])
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -3.771 -1.871 -0.171  1.654  8.254 
## 
## Coefficients:
##                                             Estimate Std. Error t value
## (Intercept)                                  8.87101    0.06612 134.170
## bd.length$Stream[bd.length$Class == "I.2"]2 -0.52472    0.21714  -2.417
##                                             Pr(>|t|)    
## (Intercept)                                   <2e-16 ***
## bd.length$Stream[bd.length$Class == "I.2"]2   0.0158 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.275 on 1303 degrees of freedom
##   (10 observations deleted due to missingness)
## Multiple R-squared:  0.004462,   Adjusted R-squared:  0.003698 
## F-statistic:  5.84 on 1 and 1303 DF,  p-value: 0.0158
## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
##  extra argument 'main' will be disregarded

## 
##  Kruskal-Wallis rank sum test
## 
## data:  bd.length$`Body length`[bd.length$Class == "I.2"] by bd.length$Stream[bd.length$Class == "I.2"]
## Kruskal-Wallis chi-squared = 5.4971, df = 1, p-value = 0.01905

##                                            Df Sum Sq Mean Sq F value
## bd.length$Stream[bd.length$Class == "II"]   1   13.2  13.165    2.82
## Residuals                                 249 1162.6   4.669        
##                                           Pr(>F)  
## bd.length$Stream[bd.length$Class == "II"] 0.0944 .
## Residuals                                         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 10 observations deleted due to missingness
## 
## Call:
## lm(formula = bd.length$`Body length`[bd.length$Class == "II"] ~ 
##     bd.length$Stream[bd.length$Class == "II"])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.6445 -1.3945  0.2555  1.5055  5.3690 
## 
## Coefficients:
##                                            Estimate Std. Error t value
## (Intercept)                                 12.0445     0.1495  80.583
## bd.length$Stream[bd.length$Class == "II"]2  -0.6135     0.3654  -1.679
##                                            Pr(>|t|)    
## (Intercept)                                  <2e-16 ***
## bd.length$Stream[bd.length$Class == "II"]2   0.0944 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.161 on 249 degrees of freedom
##   (10 observations deleted due to missingness)
## Multiple R-squared:  0.0112, Adjusted R-squared:  0.007225 
## F-statistic:  2.82 on 1 and 249 DF,  p-value: 0.09438
## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
##  extra argument 'main' will be disregarded

## 
##  Kruskal-Wallis rank sum test
## 
## data:  bd.length$`Body length`[bd.length$Class == "II"] by bd.length$Stream[bd.length$Class == "II"]
## Kruskal-Wallis chi-squared = 3.7987, df = 1, p-value = 0.05129

##                                            Df Sum Sq Mean Sq F value
## bd.length$Stream[bd.length$Class == "III"]  1    2.3   2.304   1.029
## Residuals                                  23   51.5   2.239        
##                                            Pr(>F)
## bd.length$Stream[bd.length$Class == "III"]  0.321
## Residuals                                        
## 10 observations deleted due to missingness
## 
## Call:
## lm(formula = bd.length$`Body length`[bd.length$Class == "III"] ~ 
##     bd.length$Stream[bd.length$Class == "III"])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.0571 -1.2333 -0.0333  0.4667  3.6429 
## 
## Coefficients:
##                                             Estimate Std. Error t value
## (Intercept)                                  14.6333     0.3527  41.491
## bd.length$Stream[bd.length$Class == "III"]2  -0.6762     0.6665  -1.015
##                                             Pr(>|t|)    
## (Intercept)                                   <2e-16 ***
## bd.length$Stream[bd.length$Class == "III"]2    0.321    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.496 on 23 degrees of freedom
##   (10 observations deleted due to missingness)
## Multiple R-squared:  0.04283,    Adjusted R-squared:  0.001217 
## F-statistic: 1.029 on 1 and 23 DF,  p-value: 0.3209
## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
##  extra argument 'main' will be disregarded

## 
##  Kruskal-Wallis rank sum test
## 
## data:  bd.length$`Body length`[bd.length$Class == "III"] by bd.length$Stream[bd.length$Class == "III"]
## Kruskal-Wallis chi-squared = 1.6179, df = 1, p-value = 0.2034

iv) was tadpole abundance affected by the rainfall of the previous month?